Restoration of images and 3D data to higher resolution by deconvolution with sparsity regularization

Image convolution is conventionally approximated by the LTI discrete model. It is well recognized that the higher the sampling rate, the better is the approximation. However sometimes images or 3D data are only available at a lower sampling rate due to physical constraints of the imaging system. In this paper, we model the under-sampled observation as the result of combining convolution and subsampling. Because the wavelet coefficients of piecewise smooth images tend to be sparse and well modelled by tree-like structures, we propose the L0 reweighted-L2 minimization (L0RL2 ) algorithm to solve this problem. This promotes model-based sparsity by minimizing the reweighted L2 norm, which approximates the L0 norm, and by enforcing a tree model over the weights. We test the algorithm on 3 examples: a simple ring, the cameraman image and a 3D microscope dataset; and show that good results can be obtained. © 2010 IEEE.

Convex approaches to model wavelet sparsity patterns

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees (HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity penalties that leads to convex optimizations that can be solved exactly and efficiently. We show that the methods we develop perform significantly better in de-convolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as lasso. © 2011 IEEE.

Slowness: an objective for spike-timing-dependent plasticity?

Our nervous system can efficiently recognize objects in spite of changes in contextual variables such as perspective or lighting conditions. Several lines of research have proposed that this ability for invariant recognition is learned by exploiting the fact that object identities typically vary more slowly in time than contextual variables or noise. Here, we study the question of how this "temporal stability" or "slowness" approach can be implemented within the limits of biologically realistic spike-based learning rules. We first show that slow feature analysis, an algorithm that is based on slowness, can be implemented in linear continuous model neurons by means of a modified Hebbian learning rule. This approach provides a link to the trace rule, which is another implementation of slowness learning. Then, we show analytically that for linear Poisson neurons, slowness learning can be implemented by spike-timing-dependent plasticity (STDP) with a specific learning window. By studying the learning dynamics of STDP, we show that for functional interpretations of STDP, it is not the learning window alone that is relevant but rather the convolution of the learning window with the postsynaptic potential. We then derive STDP learning windows that implement slow feature analysis and the "trace rule." The resulting learning windows are compatible with physiological data both in shape and timescale. Moreover, our analysis shows that the learning window can be split into two functionally different components that are sensitive to reversible and irreversible aspects of the input statistics, respectively. The theory indicates that irreversible input statistics are not in favor of stable weight distributions but may generate oscillatory weight dynamics. Our analysis offers a novel interpretation for the functional role of STDP in physiological neurons.

Transient response of structures with uncertain properties to nonlinear shock loading

A method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading. The displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself, expressed in terms of a nonlinear Hertzian contact stiffness. Application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only. The theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam, a plate, a thin and a thick cylinder and for the impact between two cylinders. The modal density of the flexural modes for a thick slender cylinder is derived analytically. Good agreement is found between experimental, simulated and published results, showing the reliability of the method for a wide range of situations including impacts and pyroshock applications. © 2013 Elsevier Ltd. All rights reserved.

Predicting the response of structures to transient shock loading.

This work concerns the prediction of the response of an uncertain structure to a load of short duration. Assuming an ensemble of structures with small random variations about a nominal form, a mean impulse response can be found using only the modal density of the structure. The mean impulse response turns out to be the same as the response of an infinite structure: the response is calculated by taking into account the direct field only, without reflections. Considering the short duration of an impulsive loading, the approach is reasonable before the effect of the reverberant field becomes important. The convolution between the mean impulse response and the shock loading is solved in discrete time to calculate the response at the driving point and at remote points. Experimental and numerical examples are presented to validate the theory presented for simple structures such as beams, plates, and cylinders.

Infection and propagation of lymphocystis virus isolated from the cultured flounder Paralichthys olivaceus in grass carp cell lines

The causative agent of lymphocystis disease that frequently occurs in cultured flounder Paralichthys olivaceus in China is lymphocystis virus (LV). In this study, 13 fish cell lines were tested for their susceptibility to LV. Of these, 2 cell lines derived from the freshwater grass carp Ctenopharyngodon idellus proved susceptible to the LV, and 1 cell line, GCO (grass carp ovary), was therefore used to replicate and propagate the virus. An obvious cytopathic effect (CPE) was first observed in cell monolayers at 1 d post-inoculation, and at 3 d this had extended to about 75% of the cell monolayer. However, no further CPE extension was observed after 4 d. Cytopathic characteristics induced by the LV were detected by Giemsa staining and fluorescence microscopic observation with Hoechst 33258 staining. The propagated virus particles were also observed by electron microscopy. Ultrastructure analysis revealed several distinct cellular changes, such as chromatin compaction and margination, vesicle formation, cell-surface convolution, nuclear fragmentation and the occurrence of characteristic 'blebs' and cell fusion. This study provides a detailed report of LV infection and propagation in a freshwater fish cell line, and presents direct electron microscopy evidence for propagation of the virus in infected cells. A possible process by which the CPEs are controlled is suggested.

Disentangling mechanical and mass effects on nanomechanical resonators

Micro and nanomechanical resonators are powerful and label-free sensors of analytes in various environments. Their response, however, is a convolution of mass, rigidity, and nanoscale heterogeneity of adsorbates. Here we demonstrate a procedure to disentangle this complex sensor response, to simultaneously measure both mass and elastic properties of nanometer thick samples. This turns an apparent disadvantage of these resonators into a striking and unique asset, enabling them to measure more than mass alone.

基于半马尔科夫条件随机场的命名体识别及其关系抽取研究

随着互联网和电子化办公的发展，出现了大量的文本资源。信息抽取技术可以帮助人们快速获取大规模文本中的有用信息。命名体识别与关系抽取是信息抽取的两个基本任务。本文在调研当前命名体识别和实体关系抽取中采用的主要方法的基础上，分别给出了解决方案。论文开展的主要工作有：（1）从模型选择和特征选择两个方面总结了命名体识别及实体关系抽取的国内外研究现状，重点介绍用于命名体识别的统计学习方法以及用于实体关系抽取的基于核的方法。（2）针对当前命名体识别中命名体片段边界的确定问题，研究了如何将 Semi-Markov CRFs 模型应用于中文命名体识别。这种模型只要求段间遵循马尔科夫规则，而段内的文本之间则可以被灵活的赋予各种规则。将这种模型用于中文命名体识别任务时，我们可以更有效更自由的设计出各种有利于识别出命名体片段边界的特征。实验表明，加入段相关的特征后，命名体识别的性能提高了 4-5 个百分点。（3）实体关系抽取的任务是判别两个实体之间的语义关系。之前的研究已经表明，待判别关系的两个实体间的语法树结构对于确定二者的关系类别是非常有用的，而相对成熟的基于平面特征的关系抽取方法在充分提取语法树结构特征方面的能力有限，因此，本文研究了基于核的中文实体关系抽取方法。针对中文特点，我们探讨了卷积（Convolution）核中使用不同的语法树对中文实体关系抽取性能的影响，构造了几种基于卷积核的复合核，改进了最短路依赖核。因为核方法开始被用于英文关系抽取时，F1 值也只有40%左右，而我们只使用作用在语法树上的卷积核时，中文关系抽取的F1 值达到了35%，可见核方法对中文关系抽取也是有效的。

Global Translation Preferred Active Contour

具有全局平移优先属性的主动轮廓更适于目标跟踪。演化轮廓具有的全局平移优先性可以理解为沿轮廓的速度场具有相等的倾向。根据此思想,通过定义在曲线扰动集合上的新内积空间导出了一种简单,具有平移优先的梯度流。新的内积空间由于是通过向H0主动轮廓对应的內积空间引入曲线扰动的方差获得,所以此主动轮廓称为方差主动轮廓。方差主动轮廓是将H0主动轮廓与其对应的平均梯度流通过加权求和获得,而H1主动轮廓则是通过H0主动轮廓与特定类型的核函数进行卷积得到。因此方差主动轮廓实现时更简单和快速。最后给出了H0,H1和方差主动轮廓在频域与时域的分析。

地震岩性与物性联合反演技术研究和应用

This paper studies how to more effectively invert seismic data and predict reservoir under complicated sedimentary environment, complex rock physical relationships and fewer drills in offshore areas of China. Based on rock physical and seismic amplitude-preserving process, and according to depositional system and laws of hydrocarbon reservoir, in the light of feature of seismic inversion methods present applied, series methods were studied. A joint inversion technology for complex geological condition had been presented, at the same time the process and method system for reservoir prediction had been established. This method consists four key parts. 1)We presented the new conception called generalized wave impedance, established corresponding inversion process, and provided technical means for joint inversion lithology and petrophysical on complex geological condition. 2)At the aspect of high-resolution nonlinear seismic wave impedance joint inversion, this method used a multistage nonlinear seismic convolution model rather than conventional primary structure Robinson seismic convolution model, and used Caianiello neural network implement inversion. Based on the definition of multistage positive and negative wavelet, it adopted both deterministic and statistical physical mechanism, direct inversion and indirect inversion. It integrated geological knowledge, rock physical theory, well data, and seismic data, and improved the resolution and anti-noise ability of wave impedence inversion. 3)At the aspect of high-resolution nonlinear reservoir physical property joint inversion, this method used nonlinear rock physical model which introduced convolution model into the relationship between wave impedance and porosity/clay. Through multistage decomposition, it handles separately the large- and small-scale components of the impedance-porosity/clay relationships to achieve more accurate rock physical relationships. By means of bidirectional edge detection with wavelets, it uses the Caianiello neural network to finish statistical inversion with combined applications of model-based and deconvolution-based methods. The resulted joint inversion scheme can integrate seismic data, well data, rock physical theory, and geological knowledge for estimation of high-resolution petrophysical parameters. 4)At the aspect of risk assessment of lateral reservoir prediction, this method integrated the seismic lithology identification, petrophysical prediction, multi-scale decomposition of petrophysical parameters, P- and H-spectra, and the match relationship of data got from seismics, well logging and geology. It could describe the complexity of medium preferably. Through applications of the joint inversion of seismic data for lithologic and petrophysical parameters in several selected target areas, the resulted high-resolution lithologic and petrophysical sections(impedance, porosity, clay) show that the joint inversion can significantly improve the spatial description of reservoirs in data sets involving complex deposits. It proved the validity and practicality of this method adequately.

高分辨率非线性岩性物性联合反演方法和应用

In the prediction of complex reservoir with high heterogeneities in lithologic and petrophysical properties, because of inexact data (e.g., information-overlapping, information-incomplete, and noise-contaminated) and ambiguous physical relationship, inversion results suffer from non-uniqueness, instability and uncertainty. Thus, the reservoir prediction technologies based on the linear assumptions are unsuited for these complex areas. Based on the limitations of conventional technologies, the thesis conducts a series of researches on various kernel problems such as inversions from band-limited seismic data, inversion resolution, inversion stability, and ambiguous physical relationship. The thesis combines deterministic, statistical and nonlinear theories of geophysics, and integrates geological information, rock physics, well data and seismic data to predict lithologic and petrophysical parameters. The joint inversion technology is suited for the areas with complex depositional environment and complex rock-physical relationship. Combining nonlinear multistage Robinson seismic convolution model with unconventional Caianiello neural network, the thesis implements the unification of the deterministic and statistical inversion. Through Robinson seismic convolution model and nonlinear self-affine transform, the deterministic inversion is implemented by establishing a deterministic relationship between seismic impedance and seismic responses. So, this can ensure inversion reliability. Furthermore, through multistage seismic wavelet (MSW)/seismic inverse wavelet (MSIW) and Caianiello neural network, the statistical inversion is implemented by establishing a statistical relationship between seismic impedance and seismic responses. Thus, this can ensure the anti-noise ability. In this thesis, direct and indirect inversion modes are alternately used to estimate and revise the impedance value. Direct inversion result is used as the initial value of indirect inversion and finally high-resolution impedance profile is achieved by indirect inversion. This largely enhances inversion precision. In the thesis, a nonlinear rock physics convolution model is adopted to establish a relationship between impedance and porosity/clay-content. Through multistage decomposition and bidirectional edge wavelet detection, it can depict more complex rock physical relationship. Moreover, it uses the Caianiello neural network to implement the combination of deterministic inversion, statistical inversion and nonlinear theory. Last, by combined applications of direct inversion based on vertical edge detection wavelet and indirect inversion based on lateral edge detection wavelet, it implements the integrative application of geological information, well data and seismic impedance for estimation of high-resolution petrophysical parameters (porosity/clay-content). These inversion results can be used to reservoir prediction and characterization. Multi-well constrains and separate-frequency inversion modes are adopted in the thesis. The analyses of these sections of lithologic and petrophysical properties show that the low-frequency sections reflect the macro structure of the strata, while the middle/high-frequency sections reflect the detailed structure of the strata. Therefore, the high-resolution sections can be used to recognize the boundary of sand body and to predict the hydrocarbon zones.

奇异性分析方法及其在储层预测中的应用研究

In research field of oil geophysical prospecting, reservoir prediction is refers to forecasting physical properties of petroleum reservoir by using data of seismic and well logging, it is a research which can guide oil field development. Singularities of seismic and logging data are caused by the heterogeneity of reservoir physical property. It's one of important methods that using singularity characteristics of seismic and logging data to study the reservoir physical property in recently. Among them, realization of reservoir quantitative prediction by analyzing singularity of the data and enhancing transition description of data is difficulty in method research. Based on wavelet transform and the fractal theory, the paper studied the singularity judgment criterion for seismic and logging data, not only analyzed quantitative relation between singularity data and reservoir physical property, but also applied it in practical reservoir prediction. The main achievements are: 1. A new method which provides singular points and their strength information estimation at only one single scale is proposed by Herrmann (1999). Based on that, the dissertation proposed modified algorithm which realized singularity polarity detection. 2. The dissertation introduced onset function to generalize the traditional geologic boundaries variations model which used singularity characteristics to represent the abruptness of the lithologic velocity transition. We show that singularity analysis reveals generic singularity information conducted from velocity or acoustic impedance to seismogram based on the convolution seismic-model theory. Theory and applications indicated that singularity information calculated from seismic data was a natural attribute for delineating stratigraphy boundaries due to its excellent ability in detecting detailed geologic features. We demonstrated that singularity analysis was a powerful tool to delineate stratigraphy boundaries and inverse acoustic impedance and velocity. 3. The geologic significances of logging data singularity information were also presented. According to our analysis, the positions of singularities indicate the sequence stratigraphic boundary, and there is subtle relationship between the singularity strength and sedimentary environment, meanwhile the singularity polarity used to recognize stratigraphic base-level cycle. Based on all those above, a new method which provided sedimentary cycle analysis based on the singularity information of logging data in multiple scales was proposed in this dissertation. This method provided a quantitative tool for judging interface of stratum sequence and achieved good results in the actual application.

地质规律约束下的波阻抗反演

Impedance inversion is very important in seismic technology. It is based on seismic profile. Good inversion result is derived from high quality seismic profile, which is formed using high resolution imaging resolution. High-resolution process demands that signal/noise ratio is high. It is very important for seismic inversion to improve signal/noise ratio. the main idea is that the physical parameter (wave impedance), which describes the stratigraphy directly, is achieved from seismic data expressing structural style indirectly. The solution of impedance inversion technology, which is based on convolution model, is arbitrary. It is a good way to apply the priori information as the restricted condition in inversion. An updated impedance inversion technology is presented which overcome the flaw of traditional model and highlight the influence of structure. Considering impedance inversion restricted by sedimentary model, layer filling style and congruence relation, the impedance model is built. So the impedance inversion restricted by geological rule could be realized. there are some innovations in this dissertation: 1. The best migration aperture is achieved from the included angle of time surface of diffracted wave and reflected wave. Restricted by structural model, the dip of time surface of reflected wave and diffracted wave is given. 2. The conventional method of FXY forcasting noise is updated, and the signal/noise ratio is improved. 3. Considering the characteristic of probability distribution of seismic data and geological events fully, an object function is constructed using the theory of Bayes estimation as the criterion. The mathematics is used here to describe the content of practice theory. 4. Considering the influence of structure, the seismic profile is interpreted to build the model of structure. A series of structure model is built. So as the impedance model. The high frequency of inversion is controlled by the geological rule. 5. Conjugate gradient method is selected to improve resolving process for it fit the demands of geophysics, and the efficiency of algorithm is enhanced. As the geological information is used fully, the result of impedance inversion is reasonable and complex reservoir could be forecasted further perfectly.

用宽频带远震体波波形研究中国及邻近地区地壳构造及地质意义初探

The theory and approach of the broadband teleseismic body waveform inversion are expatiated in this paper, and the defining the crust structure's methods are developed. Based on the teleseismic P-wave data, the theoretic image of the P-wave radical component is calculated via the convolution of the teleseismic P-wave vertical component and the transform function, and thereby a P-wavefrom inversion method is built. The applied results show the approach effective, stable and its resolution high. The exact and reliable teleseismic P waveforms recorded by CDSN and IRIS and its geodynamics are utilized to obtain China and its vicinage lithospheric transfer functions, this region ithospheric structure is inverted through the inversion of reliable transfer functions, the new knowledge about the deep structure of China and its vicinage is obtained, and the reliable seismological evidence is provided to reveal the geodynamic evolution processes and set up the continental collisional theory. The major studies are as follows: Two important methods to study crustal and upper mantle structure -- body wave travel-time inversion and waveform modeling are reviewed systematically. Based on ray theory, travel-time inversion is characterized by simplicity, crustal and upper mantle velocity model can be obtained by using 1-D travel-time inversion preliminary, which introduces the reference model for studying focal location, focal mechanism, and fine structure of crustal and upper mantle. The large-scale lateral inhomogeneity of crustal and upper mantle can be obtained by three-dimensional t ravel-time seismic tomography. Based on elastic dynamics, through the fitting between theoretical seismogram and observed seismogram, waveform modeling can interpret the detail waveform and further uncover one-dimensional fine structure and lateral variation of crustal and upper mantle, especially the media characteristics of singular zones of ray. Whatever travel-time inversion and waveform modeling is supposed under certain approximate conditions, with respective advantages and disadvantages, and provide convincing structure information for elucidating physical and chemical features and geodynamic processes of crustal and upper mantle. Because the direct wave, surface wave, and refraction wave have lower resolution in investigating seismic velocity transitional zone, which is inadequate to study seismic discontinuities. On the contrary, both the converse and reflected wave, which sample the discontinuities directly, must be carefully picked up from seismogram to constrain the velocity transitional zones. Not only can the converse wave and reflected wave study the crustal structure, but also investigate the upper mantle discontinuities. There are a number of global and regional seismic discontinuities in the crustal and upper mantle, which plays a significant role in understanding physical and chemical properties and geodynamic processes of crustal and upper mantle. The broadband teleseismic P waveform inversion is studied particularly. The teleseismic P waveforms contain a lot of information related to source time function, near-source structure, propagation effect through the mantle, receiver structure, and instrument response, receiver function is isolated form teleseismic P waveform through the vector rotation of horizontal components into ray direction and the deconvolution of vertical component from the radial and tangential components of ground motion, the resulting time series is dominated by local receiver structure effect, and is hardly irrelevant to source and deep mantle effects. Receiver function is horizontal response, which eliminate multiple P wave reflection and retain direct wave and P-S converted waves, and is sensitive to the vertical variation of S wave velocity. Velocity structure beneath a seismic station has different response to radial and vertical component of an accident teleseismic P wave. To avoid the limits caused by a simplified assumption on the vertical response, the receiver function method is mended. In the frequency domain, the transfer function is showed by the ratio of radical response and vertical response of the media to P wave. In the time domain, the radial synthetic waveform can be obtained by the convolution of the transfer function with the vertical wave. In order to overcome the numerical instability, generalized reflection and transmission coefficient matrix method is applied to calculate the synthetic waveform so that all multi-reflection and phase conversion response can be included. A new inversion method, VFSA-LM method, is used in this study, which successfully combines very fast simulated annealing method (VFSA) with damped least square inversion method (LM). Synthetic waveform inversion test confirms its effectiveness and efficiency. Broadband teleseismic P waveform inversion is applied in lithospheric velocity study of China and its vicinage. According to the data of high quality CDSN and IRIS, we obtained an outline map showing the distribution of Asian continental crustal thickness. Based on these results gained, the features of distribution of the crustal thickness and outline of crustal structure under the Asian continent have been analyzed and studied. Finally, this paper advances the principal characteristics of the Asian continental crust. There exist four vast areas of relatively minor variations in the crustal thickness, namely, northern, eastern southern and central areas of Asian crust. As a byproduct, the earthquake location is discussed, Which is a basic issue in seismology. Because of the strong trade-off between the assumed initial time and focal depth and the nonlinear of the inversion problems, this issue is not settled at all. Aimed at the problem, a new earthquake location method named SAMS method is presented, In which, the objective function is the absolute value of the remnants of travel times together with the arrival times and use the Fast Simulated Annealing method is used to inverse. Applied in the Chi-Chi event relocation of Taiwan occurred on Sep 21, 2000, the results show that the SAMS method not only can reduce the effects of the trade-off between the initial time and focal depth, but can get better stability and resolving power. At the end of the paper, the inverse Q filtering method for compensating attenuation and frequency dispersion used in the seismic section of depth domain is discussed. According to the forward and inverse results of synthesized seismic records, our Q filtrating operator of the depth domain is consistent with the seismic laws in the absorbing media, which not only considers the effect of the media absorbing of the waves, but also fits the deformation laws, namely the frequency dispersion of the body wave. Two post stacked profiles about 60KM, a neritic area of China processed, the result shows that after the forward Q filtering of the depth domain, the wide of the wavelet of the middle and deep layers is compressed, the resolution and signal noise ratio are enhanced, and the primary sharp and energy distribution of the profile are retained.

基于信息重建技术的地震信号处理方法研究

The dissertation addressed the problems of signals reconstruction and data restoration in seismic data processing, which takes the representation methods of signal as the main clue, and take the seismic information reconstruction (signals separation and trace interpolation) as the core. On the natural bases signal representation, I present the ICA fundamentals, algorithms and its original applications to nature earth quake signals separation and survey seismic signals separation. On determinative bases signal representation, the paper proposed seismic dada reconstruction least square inversion regularization methods, sparseness constraints, pre-conditioned conjugate gradient methods, and their applications to seismic de-convolution, Radon transformation, et. al. The core contents are about de-alias uneven seismic data reconstruction algorithm and its application to seismic interpolation. Although the dissertation discussed two cases of signal representation, they can be integrated into one frame, because they both deal with the signals or information restoration, the former reconstructing original signals from mixed signals, the later reconstructing whole data from sparse or irregular data. The goal of them is same to provide pre-processing methods and post-processing method for seismic pre-stack depth migration. ICA can separate the original signals from mixed signals by them, or abstract the basic structure from analyzed data. I surveyed the fundamental, algorithms and applications of ICA. Compared with KL transformation, I proposed the independent components transformation concept (ICT). On basis of the ne-entropy measurement of independence, I implemented the FastICA and improved it by covariance matrix. By analyzing the characteristics of the seismic signals, I introduced ICA into seismic signal processing firstly in Geophysical community, and implemented the noise separation from seismic signal. Synthetic and real data examples show the usability of ICA to seismic signal processing and initial effects are achieved. The application of ICA to separation quake conversion wave from multiple in sedimentary area is made, which demonstrates good effects, so more reasonable interpretation of underground un-continuity is got. The results show the perspective of application of ICA to Geophysical signal processing. By virtue of the relationship between ICA and Blind Deconvolution , I surveyed the seismic blind deconvolution, and discussed the perspective of applying ICA to seismic blind deconvolution with two possible solutions. The relationship of PC A, ICA and wavelet transform is claimed. It is proved that reconstruction of wavelet prototype functions is Lie group representation. By the way, over-sampled wavelet transform is proposed to enhance the seismic data resolution, which is validated by numerical examples. The key of pre-stack depth migration is the regularization of pre-stack seismic data. As a main procedure, seismic interpolation and missing data reconstruction are necessary. Firstly, I review the seismic imaging methods in order to argue the critical effect of regularization. By review of the seismic interpolation algorithms, I acclaim that de-alias uneven data reconstruction is still a challenge. The fundamental of seismic reconstruction is discussed firstly. Then sparseness constraint on least square inversion and preconditioned conjugate gradient solver are studied and implemented. Choosing constraint item with Cauchy distribution, I programmed PCG algorithm and implement sparse seismic deconvolution, high resolution Radon Transformation by PCG, which is prepared for seismic data reconstruction. About seismic interpolation, dealias even data interpolation and uneven data reconstruction are very good respectively, however they can not be combined each other. In this paper, a novel Fourier transform based method and a algorithm have been proposed, which could reconstruct both uneven and alias seismic data. I formulated band-limited data reconstruction as minimum norm least squares inversion problem where an adaptive DFT-weighted norm regularization term is used. The inverse problem is solved by pre-conditional conjugate gradient method, which makes the solutions stable and convergent quickly. Based on the assumption that seismic data are consisted of finite linear events, from sampling theorem, alias events can be attenuated via LS weight predicted linearly from low frequency. Three application issues are discussed on even gap trace interpolation, uneven gap filling, high frequency trace reconstruction from low frequency data trace constrained by few high frequency traces. Both synthetic and real data numerical examples show the proposed method is valid, efficient and applicable. The research is valuable to seismic data regularization and cross well seismic. To meet 3D shot profile depth migration request for data, schemes must be taken to make the data even and fitting the velocity dataset. The methods of this paper are used to interpolate and extrapolate the shot gathers instead of simply embedding zero traces. So, the aperture of migration is enlarged and the migration effect is improved. The results show the effectiveness and the practicability.